day 2 Quadratic Word Problems

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

Describe the transformation of the graph y = (x - 3)² - 2.

Back

The graph is shifted right 3 units and down 2 units.

Front

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex of the parabola, which occurs at x = -b/(2a) for the standard form ax² + bx + c.

Front

What does the 'a' value in a quadratic function indicate about the graph?

Back

The 'a' value indicates the direction of the parabola: if 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the x-intercepts of a quadratic function?

Back

The x-intercepts represent the points where the graph crosses the x-axis, indicating the solutions to the equation when y = 0.

Front

How can you determine the height of an object at a given time using a quadratic function?

Back

Substitute the time value into the quadratic function to find the corresponding height.

Front

What is the formula to calculate the profit from selling tickets based on ticket price?

Back

The profit can be modeled by a quadratic function, such as p = ax² + bx + c, where 'x' is the ticket price.

Front

How do you find the time it takes for an object to hit the ground using a quadratic function?

Back

Set the height function equal to zero and solve for 't' to find when the object reaches ground level.

Front

What is the maximum profit in the function p = -15x² + 600x + 60?

Back

The maximum profit can be found using the vertex formula, resulting in $6060.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.